1. Field of the Invention
This invention relates to analysis of spacecraft orbits, trajectories, and maneuvers. More specifically, the invention relates to the creation of vectors, axes, points, coordinate systems and other elements, and combinations thereof, to be used in describing the position and motion of objects in space for maneuver planning.
2. Background of the Invention
In the planning and analysis of spacecraft maneuvers, the creation of vectors, axes, points, coordinate systems and other elements and combinations thereof is required in order to describe the position and motion of rigid bodies in three-dimensional space (e.g., spacecraft orbits, trajectories, and maneuvers).
A coordinate system can itself be moving in space. It can also be attached to one or more bodies or be a solely mathematical quantity. Movements of a coordinate system can be described via functions, data files, or user input to a computer program. When a coordinate system must be created, the relationship of the new system to a pre-existing one is defined. There are many ways to define that relationship, but all must include the following: (1) a specification of how the origin of the new coordinate system is translated relative to the origin of the existing system, and (2) a specification of how the set of three orthogonal axes defining the orientation of the new system is rotated relative to the set of axes of the existing system.
This introduces two important coordinate concepts that are part of any coordinate system definition: (1) origin point, and (2) axes. Given a point in space (i.e., an “origin”) and a set of axes oriented in space, one can create a coordinate system by combining the point and the axes.
If there is a plurality of points and axes, one can create any desired combination thereof, thus increasing the number of possible coordinate systems. Advantages of a system providing this capability include: (1) reusability of the coordinate points and axes, of which a limited amount can be used to create a great number of coordinate systems, and (2) improved accuracy where two or more coordinate systems share common points and/or axes, since shared components need only be defined once, thus minimizing the possibility of error in performing duplicative computations.
Another component useful in constructing a coordinate system is the vector. The vector relates to points and axes in a number of ways. A new point can be specified by a vector starting at a pre-defined point. A new vector can be defined on the basis of two existing points, starting and ending. A new set of orthogonal axes can be specified by using two non-parallel vectors. A new vector can be created by performing various vector operations (rotation about another vector, cross-product, negation, etc.). Thus, vectors, along with points and axes, provide useful building blocks for constructing new coordinate systems.
Existing programs require users to write new computer code whenever a new coordinate relationship is introduced. Alternatively, when a graphical user interface (GUI) is provided, the choices offered by the GUI are limited to a certain subset of the myriad possibilities, thus limiting the options available for the analyst.
Some existing programs require that all relationships of interest be hard-coded, whereas some require that only one relationship be hard-coded. For example, the Jet Propulsion Laboratory (JPL) distributes the SPICE toolkit that contains a set of functions to perform coordinate conversions. The conversions can be obtained between any two of the specified coordinate frames, with each new frame specified relative to some existing frame. Nevertheless, this is a laborious task, since the specification must be performed through a file. The JPL SPICE toolkit also lacks the ability to specify points or vectors, which are crucial building blocks for interrelating various coordinate systems.
Another existing program, the Navigator software module (a product of Analytical Graphics, Inc. of Malvern, Pa.), provides a GUI for constructing coordinate systems, but is limited in that it constructs coordinate axes alone. It is not capable of constructing vectors from points nor axes from vectors. Furthermore, the Navigator module cannot construct a coordinate system from a set of axes and a point. Finally, the Navigator module has no capability to account for coordinate systems that rotate with respect to each other.
Thus, what is needed is a scheme for a spacecraft maneuver analyst to specify relationships for new coordinate systems without the need to hard-code a software solution. What is also needed is a scheme for a spacecraft maneuver analyst to model orbital maneuver phenomena according to any of a myriad of possible coordinate systems without the need to hard-code a software solution.